Why doesn't my SkyTexture show up in the preview tab?
In your world settings, do you have real sky, and environment lighting enabled? Here are the steps to get your desired results. 
Go to the world tab and click real sky, then environment lighting. Then, make sure that you have sky texture selected in the drop down menu off to the right.
Next, go to the textures tab and choose your image. Set the mapping as you already have, and click horizon, and that should do it. The world settings I use are as in the attached screenshot.
Hope that helps.